Sainsbury's chief executive, Justin King, a vocal critic of tax avoidance, has launched the supermarket's first mobile phone service with Vodafone, which has been heavily criticised for its use of tax havens.

The UK's third biggest supermarket was accused of hypocrisy over the deal, which could net Vodafone millions of pounds as Sainsbury's rents its mobile spectrum and shares the profits. It comes a week after King said the debate around tax avoidance was a "moral issue" rather than just a legal one.

On Monday King welcomed the deal with Vodafone. "Together with Vodafone, we'll be able to develop mobile products and services that represent great value for Sainsbury's customers."

Mobile by Sainsbury's is set to launch later this summer and follows similar services from rivals Tesco and Asda.

Richard Brooks, the author of The Great Tax Robbery who exposed many of Vodafone's tax avoidance tactics, questioned Sainsbury's decision and suggested it was indirectly helping Vodafone avoid tax.

"What Sainsbury's is doing is the large corporate equivalent of paying cash in hand. It might not be avoiding tax itself, but it can be pretty sure it's helping somebody else to.

"You can't scrutinise the tax affairs of everybody you deal with, but it is incredible that a company so outspoken on the morality of tax should get into bed with such a prolific tax avoider.

"Vodafone pays no tax on its current UK profits and in the shape of its finance companies in Luxembourg owns the biggest tax avoidance vehicles in the FTSE 100. One of them makes $2.5bn [£1.6bn] a year, employs less than one accountant and pays no tax."

The mobile phone provider was accused in parliament of paying just £1.25bn of an alleged £6bn tax bill which was personally negotiated between Vodafone and the then-boss of HM Revenues and Customs, Dave Hartnett, in 2010. Vodafone disputes this figure.

Last month the company revealed it paid no corporation tax in the past two years. In a nine-page document defending its position, Vodafone said: "Individuals and companies have legal obligations to pay tax, but those obligations do not extend to paying more than the amount legally required. Companies also have a legal obligation to act in the interests of their shareholders. Vodafone's shareholders include many of the investment funds relied upon by tens of millions of individual pensioners and savers."

On its website, Vodafone says: "We are a company that believes in operating according to the law, including paying our taxes."

By comparison, Sainsbury's paid £144m in corporation tax and was the 14th biggest taxpayer on the FTSE100 despite being the 46th biggest company, according to accountancy firm PwC.

Last week, King criticised companies for treating tax as only a legal issue, rather than a moral one, and said businesses risked losing customers if they adopted aggressive tax avoidance measures.

Speaking at the British Retail Consortium's annual symposium, he said: "Tax is a moral issue, I would argue. Every business in a position of trust should be able to stand up and try to explain why they arrange their affairs the way they do if they believe they have nothing to hide.

"Trust is a moral issue and you can't claim to hold a trustworthy space on any issue, including tax, by just saying 'I'm operating within the law' because it is not a good enough articulation to win trust. Of course we all operate within the law. It's shocking that anybody would think saying we operate within the law does anything other than confirm what every consumer believes to be true."

UK Uncut, which has campaigned against tax avoidance and staged sit-ins in Vodafone stores, called on Sainsbury's to reconsider the partnership.

Spokesman Damian Joyce said: "Justin King is right to criticise companies that claim it's OK to drain the public finances of vital revenues because tax avoidance is legal.

"But he's taking the moral low ground by joining forces with Vodafone, a company that allegedly avoided a £6bn tax bill that would have paid for a year's worth of welfare cuts."

The new phone service by Sainsbury's is aimed at attracting loyal customers who would be rewarded with Nectar points for signing up and comes as supermarkets attempt to cash in on extra services, including insurance and banking.

Richard Murphy, a tax expert from Tax Research UK, warned that the deal could backfire for Sainsbury's and King. "If Justin [King] was going to actually make a moral stance on this issue he should have looked to work with a company who makes a stance on this matter instead of getting into bed with them. Evidence is made by actions not words."